Semilinear elliptic equations with degenerate and singular weights related to Caffarelli–Kohn–Nirenberg inequalities

In this note we give some existence and nonexistence results of solutions to a problem of the type (Pt,p) { − div ( | x | − 2 γ ∇ u ) = λ | x | 2 ( γ + 1 ) u + u p | x | α + t f | x | 2 γ in  Ω u ≥ 0 , u ≢ 0 in  Ω u = 0 on  ∂ Ω , where Ω is an open bounded subset of R N containing the origin, the constants p , t , α , γ , λ satisfy suitable conditions and f ≢ 0 is a nonnegative, smooth bounded function on Ω . The results that will be given generalize some known results in Brezis et al. (2005) [1] and Dupaigne (2002) [2].